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**tttcomrader** Suppose that the function $\displaystyle f: \mathbb {R}^2 \rightarrow \mathbb {R} $ has the properties of:

a) $\displaystyle f(0,0)=1$

b) $\displaystyle \frac { \partial f }{ \partial x } (x,y) = 2 $ and $\displaystyle \frac { \partial f }{ \partial y } (x,y) = 3 \ \ \ \ \ \forall (x,y) \in \mathbb {R}^2 $

Prove that $\displaystyle f(x,y)=1+2x+3y$

Well, I guess I can integrate the derivatives and get this answer, but I have to solve it with methods of mean value theorem and gradients... How should I proceed? Thank you.